Alright then, here's a list of games you should get, in priority order (highest to the top you should get first). First, we go retail (Bolded are below £20, Underlined are below £10)

• Super Mario Galaxy 2
• Monster Hunter Tri
• Brawl
• Super Mario Galaxy
• Mario Kart Wii
• Donkey Kong Country Returns
• Metroid Prime Trilogy
• Fire Emblem- Radiant Dawn
• Okami
• Red Steel 2
• New Super Mario Bros. Wii
• Goldeneye
• Call Of Duty- Black Ops
• No More Heroes 2
• No More HEroes
• Klonoa
• Little King's Story
• Resident Evil 4
• Wii Sports Resort (if not in pac)
• Twilight Princess
• Sonic Colours
• Wii Party
• Tales Of Symphonia- Dawn Of The New World
• Madworld
• House Of The Dead- Overkill
• Resident Evil Chronicles
• Fragile Dreams- Farewell Ruins Of The Moon

• Zelda- Ocarina Of Time
• Zelda- Majora's Mask
• Mario 64
• Sonic 1-3
• Chrono Trigger
• Super Mario RPG- Legend Of The Seven Stars
• Donkey Kong Country
• Super Smash Bros.

Of Course, these are not all the games you should get, but it's a good starting list. Choose some of them (preferably the top ones of each list or any which intrigue you) and go from there. But there's welll over 2,000 hours worth of gaming there alone! If I HAD to choose a select few, definitely get Monster Hunter Tri and Glaxy 2 first. Maybe Okami or Goldeneye/Red Steel. As Tri takes well over 250 hours to complete, you may never need another Wii game anyway! 

Also, what made you decide to get a Wii anyway? Atany rate, for that price, why refuse it? Welcome to the club!

Sure thing, Serious_frusting!

Mario Kart Wii
Smash Bros Brawl
NSMB Wii
Donkey Kong Country Returns
Zelda: Twilight Princess
Metroid Prime 3 (I'd reccomend the Trilogy, but since Ninty stopped producing it, it's tough to find and costs a lot)
Mario Galaxy 2 (I wouldn't bother with the 1st, they are similar, yet this one is superior in almost every way).
Warioware Smooth Moves
Wii Sports Resort
Little King's Story
RE4 (the definitive version)
Monster Hunter Tri
Zack and Wiki
Dawn of Discovery
Red Steel 2

That should keep ya busy for quite awhile. Enjoy the new Wii! It's a very fun console, particularly for multiplayer

I'd try the Trauma Center games, it's one of my favourite new series from this generation.
Don't know your preferences, so I'll put some titles that aren't suggested that much.

Zach & Wiki
Elebits
Dewy's adventure
Samba De Amigo
We Ski & Snowboard
Trauma Center:New Blood/Trauma Team
The Munchables
Little King's Story
Endless Ocean 2
Just Dance 2/We Cheer
Red Steel 2
Mario & Sonic various Olympic Games

Thank you all for the suggestions. I will look into these games

Just so you know, if you don't get the Galaxy games and Tri, then you'll be making a HUGE mistake. Look at how many times they're suggested in the thread!

I have played all the monster hunter games. I have every intention in getting that game, I also intend to purchase all the mario platformers as i grew up on them and sonic. :)

Oh and I forgot...

HOUSE OF THE DEAD 2!

This is arcade shooting at it's finest, it's absolutely thrilling, even better with 2 people.

I think that's a good move. If you liked MH on the PSP you'll love the Wii version. Not so many monsters to fight or as many weapons, but all new monsters, underwater and online??? NICE

My favorite third-party games:

Red Steel 2
Lame story and mission designs, but frickin' awesome sword-fighting mechanics. And pretty.

Trauma Center
Tons of fun, if you're up for a challenge. Also a good example of a game that can only work well on Wii (and DS).

Pro Evolution Soccer
I've played several soccer games over the years, but PES on Wii is easily my favorite way to play. Pointer controls FTW.

Zack & Wiki
If you like traditional point-and-click adventures, are up for a challenge, and can stand the cutesy art style, go for it. If not, avoid.

And my favorite first-party games (need no explanations):

Metroid Prime Trilogy/3
Punch Out
Mario Kart Wii
NPC Pikmin
WarioWare

Wii fit and RE4 are the only games on wii you should get, in my opinion.